To find the product of the binomials [tex]\((5x + 2)(4x + 4)\)[/tex], let's use the distributive property to expand them step-by-step.
1. First terms: Multiply the first term from each binomial:
[tex]\[
5x \cdot 4x = 20x^2
\][/tex]
2. Outer terms: Multiply the first term from the first binomial with the second term from the second binomial:
[tex]\[
5x \cdot 4 = 20x
\][/tex]
3. Inner terms: Multiply the second term from the first binomial with the first term from the second binomial:
[tex]\[
2 \cdot 4x = 8x
\][/tex]
4. Last terms: Multiply the second term from each binomial:
[tex]\[
2 \cdot 4 = 8
\][/tex]
Next, sum these values to form the expanded polynomial:
[tex]\[
20x^2 + 20x + 8x + 8
\][/tex]
Combine the like terms [tex]\(20x\)[/tex] and [tex]\(8x\)[/tex]:
[tex]\[
20x^2 + 28x + 8
\][/tex]
Thus, the product of the binomials [tex]\((5x + 2)(4x + 4)\)[/tex] is:
[tex]\[
20x^2 + 28x + 8
\][/tex]
Therefore, the correct answer is:
[tex]\[
\text{D. } 20x^2 + 28x + 8
\][/tex]
